Offset Edge Loop Cut
Offset Edge Slide seems to behaves quite irregular. A created vertex in a corner that moves inward doesn't do so consistent with the distance of other vertices and edges, and the outward side doesn't create a vertex. (not sure how to easily change that)

But in this specific case a Bevel in combination with Knife Project might do the job:


Copy the cube object and create the edge offset by Bevel.
Select the edges you like, duplicate them, Press P and Separate by Selection to make them a separate object. Then move them over/above the original object.
In Object Mode select the edges object, then Shift select the original cube object, and (with both objects selected) go into Edit mode.
Press numpad 7 so the knife cut will be projected onto the desired surface at the right angle, in this case downward.
Apply Knife Project. In Edit Mode, 3D Viewport > Mesh > Knife Project.




Result: